FIG. 1A illustrates a circuit diagram of a conventional transformer 10 from related art. The conventional transformer 10 includes a primary transformer coil 12 and a secondary transformer coil 14. The primary transformer coil 12 and the secondary transformer coil 14 are magnetically coupled by a magnetic core (not explicitly illustrated). This arrangement is typically used in radio frequency (RF) applications where the conventional transformer 10 is provided within or on a laminated substrate along with other RF devices. More particularly, the conventional transformer 10 is operable to convert a higher voltage/lower current (HVLC) signal 16 to a lower voltage/higher current (LVHC) signal 18, and vice versa. The conventional transformer 10 also provides isolation between RF devices connected to the primary transformer coil 12 and the secondary transformer coil 14. Furthermore, an impedance transformation provided by the primary transformer coil 12 and the secondary transformer coil 14 can be used to provide impedance matching between the RF devices.
In the conventional transformer 10, the primary transformer coil 12 is the coil that receives and/or outputs the HVLC signal 16 and the secondary transformer coil 14 is the coil that receives and/or outputs the LVHC signal 18. To do this, the primary transformer coil 12 forms one or more primary windings and the secondary transformer coil 14 forms secondary windings. The ratio (i.e., the turns ratio) between the number of primary windings and secondary windings is represented in FIG. 1A as 1:n. Due to the magnetic coupling provided by the magnetic core of the conventional transformer 10, a current of the HVLC signal 16 induces a current of the LVHC signal 18 while a current of the HVLC signal 16 induces a current of the LVHC signal 18. Ideally, the current and voltage transformations between the HVLC signal 16 and the LVHC signal 18 can be expressed as:
  n  =                    V        2                    V        1              =                  I        1                    I        2            
However, non-ideal transformer behavior, particularly when the HVLC signal 16 and the LVHC signal 18 are operating in RF bands, result in transformer losses. As such, the above expression is modified due to the transformer losses resulting in the primary transformer coil 12, the secondary transformer coil 14, and the magnetic core.
FIG. 1B illustrates a transformer model 20 at RF frequencies for the conventional transformer 10 shown in FIG. 1A. The conventional transformer 10 is coupled to a source 22 and a load 24. The source 22 is modeled by a resistor Rs and a capacitor Cs while the load 24 is modeled by a resistor RL and a capacitor CL. The primary transformer coil 12 has a self-inductance of L1 (See FIG. 1A) and the secondary transformer coil 14 (See FIG. 1A) has a self-inductance of L2. To model the non ideal-behavior of the conventional transformer 10 in the transformer model 20, various components are coupled to an ideal transformer 26. For instance, the primary transformer coil 12 and the secondary transformer coil 14 are lossy. This is modeled by the resistor, R1 and the resistor R2. Furthermore, due to magnetic leakage, the primary transformer coil 12 is modeled by inductor LP and inductor, LPLEAK, while the secondary transformer coil 14 is modeled by the inductor LSLEAK. The inductor LP models the inductance that transfers energy to the secondary transformer coil 14. The inductance of the inductor LP is equal the magnetic coupling coefficient, k, multiplied by the self-inductance L1 (see FIG. 1A), of the primary transformer coil 12. The inductor LPLEAK models the parasitic magnetic leak in the primary transformer coil 14 and has an inductance that is equal to (1−k)*L1. The inductor LSLEAK models the parasitic magnetic leak in the secondary transformer coil 16 and has an inductance equal to 1−k*L2. The capacitance, CPAR, models the parasitic capacitance resulting between the primary transformer coil 12 and the secondary transformer coil 14 resulting from electric field leaks in the magnetic core. Generally, the parasitic capacitance, CPAR, increases as the frequency increases.
There are various metrics that may be utilized to express the performance of the conventional transformer 10. One of these metrics is the transformer power efficiency (TPE) of the conventional transformer 10. In the RF which can be expressed as:
  η  =            P      Load              P      Total      where,
PLoad=Power delivered to the load 24
PTotal=Total available power received from source 22
In the RF frequency range, it can be shown that the maximum efficiency of the conventional transformer 10 is maximized by satisfying the equations:
      η    max    =      1                  2                              Q            1                    ⁢                      Q            2                    ⁢                      k            2                              +                        1          +                                    2              ⁡                              [                                  1                  +                                      1                                                                  Q                        1                                            ⁢                                              Q                        2                                            ⁢                                              k                        2                                                                                            ]                                      *                          1                                                Q                  1                                ⁢                                  Q                  2                                ⁢                                  k                  2                                                                        where,
            Q      1        =                            ω          ⁢                                          ⁢                      L            1                                    R          1                    =              Quality        ⁢                                  ⁢        Factor        ⁢                                  ⁢        of        ⁢                                  ⁢        the        ⁢                                  ⁢        primary        ⁢                                  ⁢        transformer        ⁢                                  ⁢        coil        ⁢                                  ⁢        12                        Q      2        =                            ω          ⁢                                          ⁢                      L            2                                    R          2                    =              Quality        ⁢                                  ⁢        Factor        ⁢                                  ⁢        of        ⁢                                  ⁢        the        ⁢                                  ⁢        secondary        ⁢                                  ⁢        transformer        ⁢                                  ⁢        coil        ⁢                                  ⁢        14                        ω      ⁢                          ⁢              L        1              =                  R        Load                              η          2                ⁢                                            1                              Q                2                2                                      +                                          Q                1                                                              Q                  2                                ⁢                                  k                  2                                                                        
For example, the magnetic coupling coefficient k can be improved by providing thicker windings. Unfortunately, this decreases the required matching of the self-inductances, L1, L2 at the primary transformer coil 12 and the secondary transformer coil 14 set by the self-inductances L1, L2. On the other hand, increasing the self-inductances, L1, L2, to increase matching can decrease the quality factors Q1, Q2. Accordingly, matching, the quality factors, and the magnetic coupling coefficient must be balanced to maximize TPE.
While the conventional transformer 10 can provide suitable impedance transformation and low losses at lower frequencies, the conventional transformer 10 is significantly undermined at higher RF frequencies by parasitics in the magnetic core arrangement. On the other hand, transmission line transformer structures are generally not employed in RF applications due to their high cost, low quality factors, and poor magnetic coupling efficients in laminated substrates, such as printed circuit boards (PCBs).
Therefore, what is needed is a transformer structure that can provide better power efficiency at RF frequencies, particularly when the transformer is being employed in a laminated substrate.